A new proof of a lemma by Phelps

Abstract

We give a different proof of a lemma by Phelps (1960) which asserts, roughly speaking, that if two norm-one functionalsfandghave their hyperplanesf−1(0)andg−1(0)sufficiently close together, then either‖f−g‖or‖f+g‖must be small. We also extend this result to a complex Banach space.